We're getting a new laptop for the kids to use, and they love my Lenovo X1 Carbon that I use at work because it's so light -- under 3 lbs! Plus it has a great multi-touch screen. Unfortunately the graphics card is an Intel 4400. Do you think it'd run EQ OK? They both like to play occasionally, but they aren't hardcore gamers or anything.

The system requirements for Everquest are very modest; the FAQ calls for an Nvidia Ti 4800 or equivalent. The laptop you're considering is a little better than that but not by much, you'll still be in the minimum specs part of town. You'll likely need to lower the graphics in game and more modern zones might lag you a bit.

While it may be able to chug Everquest along, keep in mind that that laptop and graphics set are unsuitable for gaming in general. If you think you or the kids will ever want to play anything else, you'll likely have problems.

I have a laptop with HD4000 graphics. I play Diablo 3 on it, I've played TERA, FFXIV and WoW on it as well. Graphics on low, disabling as many intensive effects (shadows, etc) as I can. They aren't great graphics, but the games have been playable. The only screenshot from my laptop that I can find is from FFXIV beta:

You'll probably want to limit how long they game on it, as the laptop is going to produce quite a bit of heat, but I mean it's passable.